The various wave-extrapolation operators can be split into two parts,
a complicated part called the
*diffraction*
or
*migration*
part, and an easy part called the
*lens*
part. The lens equation applies a time shift that is a function of *x*.
The lens equation acquires its name because it acts just like
a thin optical lens when a light beam enters on-axis (vertically).
Corrections for nonvertical incidence
are buried somehow in the diffraction part.
The lens equation has an analytical solution,
namely, .It is better to use this analytical solution than to use a finite-difference
solution because there are no approximations in it to go bad.
The only reason the lens equation is mentioned at all in a chapter on
finite differencing is that the companion diffraction equation must be
marched forward along with the lens equation, so the analytic solutions are
marched along in small steps.

10/31/1997